Two structural models of the thermo-elastic behavior of space-reinforced media are offered at the general anisotropy of the component materials of the composition. As criteria of equivalence of fibrous composition to a fictitious homogeneous anisotropic material the equality specific free energy and the Gibbs thermodynamic energy in them are used. It allows determining the upper and lower boundaries of the effective stiffness of reinforced materials. Comparison with experiments was performed. It was shown that lower bounds for effective rigidities better agreed with the experimental data than the calculated values of the same values that are defined on the basis of other structural models.